Solve f(x, y) = x^2 y^2

Simplify

f (x, y) = x^{2} y^{2}

Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x

f_{x} = \frac{\partial}{\partial x} (x^{2} y^{2})

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

f_{x} = y^{2} \times \frac{\partial}{\partial x} (x^{2})

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

f_{x} = y^{2} \times 2 x

Solution

f_{x} = 2 x y^{2}

Function